Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 26.11.2024 06:58, Jim Burns wrote:

On 11/25/2024 8:52 AM, WM wrote:

Finite cardinalities belong to dark endsegments.

 Finite cardinals can change by 1

Yes. The last endsegments have 3, 2, 1, 0 elements.

 Each end.segment Eᶠⁱⁿ(k) of the finite.cardinalities ℕᶠⁱⁿ
holds a countable.to.from.0 least.element

No. All elements of finite endsegments  (and almost all of infinite endsegments) are dark.

The endsegments
only can have an empty intersection
if there are endsegments with 3, 2, 1, 0 elements.

 The end.segments
can only have a non.empty intersection
if there is an element which is in each end.segment.

That is the case for every non-empty endsegment before all elements are lost.
Otherwise two endsegments with different elements must exist. That is impossible by inclusion monotony.
Regards, WM